Tried to create QTextEdit inside class inherited by QThread, pass it to MainWindow, where I displayed it, but I get qDebug() "error" into Qt Creator:

Tried to create class inherited by QObject, created QTextEdit inside, adding few functions for threads, created the class in MainWindow and displayed the QTextWidget, and moved the object with moveToThread(); as it should be the "proper way". But I get the same result as at point 2.

It works, as long thread delay is larger than 2. After that it crashes.
This is one of the errors thrown into Qt Creator:
@ASSERT failure in QVector<T>::operator[]: "index out of range", file ....\include/QtCore/../../src/corelib/tools/qvector.h, line 359
Invalid parameter passed to C runtime function.@

At point 2 and 3, there is also problem with windows resizing. There is a pretty big possibility that it crashes when resizing on X axis while thread running.

The reason I'm not using emitors is, that they are slow, and the program crashes sooner that at options two.

You cannot have any GUI elements outside the main thread. If you want to manipulate GUI elements from other threads you either have to use signals and slots or you have to use invokeMethod(Qt::QueuedConnection) to call the slot, for example QTextEdit::setText(), directly.